Subgroups — C₁₃×#8265 #15694604

Order 3328.

438 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1744	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#322	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#322	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1273	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1273	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×C₄⋊C₈	C₄	1	2	yes	—
9	C₂×C₁₃×C₄⋊C₈	C₄	1	2	yes	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₄³×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#336	C₄	1	2	yes	—
18	C₁₃×#336	C₄	1	2	yes	—
19	C₁₃×#336	C₄	1	2	yes	—
20	C₁₃×#336	C₄	1	2	yes	—
21	C₁₃×#322	—	2	2	no	—
22	C₁₃×#322	—	2	2	no	—
23	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
25	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
26	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
27	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
28	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
36	C₁₃×C₄⋊C₈	—	2	4	no	—
37	C₁₃×C₄⋊C₈	—	2	4	no	—
38	C₄×C₈×C₁₃	—	2	1	no	—
39	C₄×C₈×C₁₃	—	2	1	no	—
40	C₄×C₈×C₁₃	—	2	1	no	—
41	C₄×C₈×C₁₃	—	2	1	no	—
42	C₄×C₈×C₁₃	—	2	1	no	—
43	C₄×C₈×C₁₃	—	2	1	no	—
44	C₄×C₈×C₁₃	—	2	1	no	—
45	C₄×C₈×C₁₃	—	2	1	no	—
46	C₄×C₈×C₁₃	—	2	1	no	—
47	C₄×C₈×C₁₃	—	2	1	no	—
48	C₄×C₈×C₁₃	D₄	1	2	yes	—
49	C₄×C₈×C₁₃	Q₈	1	2	yes	—
50	#8265	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
53	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₈×C₁₃	—	2	2	no	—
59	C₂×C₈×C₁₃	—	2	2	no	—
60	C₂×C₈×C₁₃	—	2	2	no	—
61	C₂×C₈×C₁₃	—	2	2	no	—
62	C₂×C₈×C₁₃	—	2	2	no	—
63	C₂×C₈×C₁₃	—	2	2	no	—
64	C₂×C₈×C₁₃	—	2	2	no	—
65	C₂×C₈×C₁₃	—	2	2	no	—
66	C₂×C₈×C₁₃	—	2	2	no	—
67	C₂×C₈×C₁₃	—	2	2	no	—
68	C₂×C₈×C₁₃	—	2	2	no	—
69	C₂×C₈×C₁₃	—	2	2	no	—
70	C₂×C₈×C₁₃	—	2	2	no	—
71	C₂×C₈×C₁₃	—	2	2	no	—
72	C₂×C₈×C₁₃	—	2	2	no	—
73	C₂×C₈×C₁₃	—	2	2	no	—
74	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
75	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
76	C₄²×C₁₃	—	2	2	no	—
77	C₄²×C₁₃	—	2	2	no	—
78	C₄²×C₁₃	—	2	2	no	—
79	C₄²×C₁₃	—	2	2	no	—
80	C₄²×C₁₃	—	2	2	no	—
81	C₄²×C₁₃	M₁₆	1	4	yes	—
82	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
83	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
84	C₄²×C₁₃	#41	1	1	yes	characteristic
85	C₄²×C₁₃	#41	1	1	yes	characteristic
86	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
87	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
88	#1744	C₂×C₁₃	1	1	yes	characteristic
89	C₂×#322	C₂×C₁₃	1	1	yes	characteristic
90	C₂×#322	C₂×C₁₃	1	1	yes	characteristic
91	#1273	C₂×C₁₃	1	1	yes	characteristic
92	#1273	C₂×C₁₃	1	1	yes	characteristic
93	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
94	C₂×C₄×C₁₃	—	2	1	no	—
95	C₂×C₄×C₁₃	—	2	1	no	—
96	C₂×C₄×C₁₃	—	2	1	no	—
97	C₂×C₄×C₁₃	—	2	1	no	—
98	C₂×C₄×C₁₃	—	2	1	no	—
99	C₂×C₄×C₁₃	—	2	1	no	—
100	C₂×C₄×C₁₃	—	2	1	no	—
101	C₂×C₄×C₁₃	—	2	1	no	—
102	C₂×C₄×C₁₃	—	2	1	no	—
103	C₂×C₄×C₁₃	—	2	1	no	—
104	C₂×C₄×C₁₃	#97	1	2	yes	—
105	C₂×C₄×C₁₃	#97	1	2	yes	—
106	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
108	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
109	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
110	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
111	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
112	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
113	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
114	C₂×C₄×C₁₃	#131	1	2	yes	—
115	C₂×C₄×C₁₃	#131	1	2	yes	—
116	C₂×C₄×C₁₃	#131	1	2	yes	—
117	C₂×C₄×C₁₃	#131	1	2	yes	—
118	C₈×C₁₃	—	2	4	no	—
119	C₈×C₁₃	—	2	4	no	—
120	C₈×C₁₃	—	4	2	no	—
121	C₈×C₁₃	—	4	2	no	—
122	C₈×C₁₃	—	4	2	no	—
123	C₈×C₁₃	—	4	2	no	—
124	C₂×C₄⋊C₈	C₄×C₁₃	1	2	yes	—
125	C₂×C₄⋊C₈	C₄×C₁₃	1	2	yes	—
126	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
127	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
128	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
129	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
130	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
131	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
132	C₄³	C₂²×C₁₃	1	1	yes	characteristic
133	#336	C₄×C₁₃	1	2	yes	—
134	#336	C₄×C₁₃	1	2	yes	—
135	#336	C₄×C₁₃	1	2	yes	—
136	#336	C₄×C₁₃	1	2	yes	—
137	#322	—	2	2	no	—
138	#322	—	2	2	no	—
139	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
140	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
141	C₂²×C₁₃	C₄×M₁₆	1	1	yes	characteristic
142	C₂²×C₁₃	#405	1	1	yes	characteristic
143	C₂²×C₁₃	#405	1	1	yes	characteristic
144	C₂²×C₁₃	#405	1	1	yes	characteristic
145	C₂²×C₁₃	#405	1	1	yes	characteristic
146	C₄×C₁₃	—	2	2	no	—
147	C₄×C₁₃	—	2	2	no	—
148	C₄×C₁₃	—	4	1	no	—
149	C₄×C₁₃	—	4	1	no	—
150	C₄×C₁₃	#424	1	2	yes	—
151	C₄×C₁₃	#433	1	2	yes	—
152	C₄×C₁₃	#435	1	2	yes	—
153	C₄×C₁₃	#436	1	2	yes	—
154	C₄×C₁₃	#446	1	2	yes	—
155	C₄×C₁₃	#446	1	2	yes	—
156	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
157	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
158	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
159	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
160	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
161	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
162	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
163	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
164	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
165	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
166	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
167	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
168	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
169	C₄⋊C₈	—	2	4	no	—
170	C₄⋊C₈	—	2	4	no	—
171	C₄×C₈	—	2	1	no	—
172	C₄×C₈	—	2	1	no	—
173	C₄×C₈	—	2	1	no	—
174	C₄×C₈	—	2	1	no	—
175	C₄×C₈	—	2	1	no	—
176	C₄×C₈	—	2	1	no	—
177	C₄×C₈	—	2	1	no	—
178	C₄×C₈	—	2	1	no	—
179	C₄×C₈	—	2	1	no	—
180	C₄×C₈	—	2	1	no	—
181	C₄×C₈	D₄×C₁₃	1	2	yes	—
182	C₄×C₈	Q₈×C₁₃	1	2	yes	—
183	C₂×C₁₃	#1451	1	1	yes	characteristic
184	C₂×C₁₃	#1452	1	1	yes	characteristic
185	C₂×C₁₃	#1453	1	1	yes	characteristic
186	C₂×C₁₃	#1454	1	1	yes	characteristic
187	C₂×C₁₃	#1768	1	1	yes	characteristic
188	C₂×C₁₃	#1770	1	1	yes	characteristic
189	C₂×C₁₃	#1771	1	1	yes	characteristic
190	C₂²×C₄	C₄²×C₁₃	1	1	yes	characteristic
191	C₂²×C₄	C₄²×C₁₃	1	1	yes	characteristic
192	C₂²×C₄	C₄²×C₁₃	1	1	yes	characteristic
193	C₂²×C₄	C₄²×C₁₃	1	1	yes	characteristic
194	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
195	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
196	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	2	2	no	—
199	C₂×C₈	—	2	2	no	—
200	C₂×C₈	—	2	2	no	—
201	C₂×C₈	—	2	2	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	2	2	no	—
204	C₂×C₈	—	2	2	no	—
205	C₂×C₈	—	2	2	no	—
206	C₂×C₈	—	2	2	no	—
207	C₂×C₈	—	2	2	no	—
208	C₂×C₈	—	2	2	no	—
209	C₂×C₈	—	2	2	no	—
210	C₂×C₈	—	2	2	no	—
211	C₂×C₈	—	2	2	no	—
212	C₂×C₈	—	2	2	no	—
213	C₂×C₈	C₁₃×C₄⋊C₄	1	4	yes	—
214	C₂×C₈	C₁₃×M₁₆	1	4	yes	—
215	C₄²	—	2	2	no	—
216	C₄²	—	2	2	no	—
217	C₄²	—	2	2	no	—
218	C₄²	—	2	2	no	—
219	C₄²	—	2	2	no	—
220	C₄²	C₁₃×M₁₆	1	4	yes	—
221	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
222	C₄²	C₂×Q₈×C₁₃	1	1	yes	characteristic
223	C₄²	C₁₃×#41	1	1	yes	characteristic
224	C₄²	C₁₃×#41	1	1	yes	characteristic
225	C₁₃	#8265	1	1	yes	characteristic, direct product factor, Sylow
226	C₂³	C₂×C₄²×C₁₃	1	1	yes	characteristic
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	2	1	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	2	1	no	—
235	C₂×C₄	—	2	1	no	—
236	C₂×C₄	—	2	1	no	—
237	C₂×C₄	C₁₃×#97	1	2	yes	—
238	C₂×C₄	C₁₃×#97	1	2	yes	—
239	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
240	C₂×C₄	C₁₃×#117	1	1	yes	characteristic
241	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
242	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
243	C₂×C₄	C₄×Q₈×C₁₃	1	1	yes	characteristic
244	C₂×C₄	C₄×Q₈×C₁₃	1	1	yes	characteristic
245	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
246	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
247	C₂×C₄	C₁₃×#131	1	2	yes	—
248	C₂×C₄	C₁₃×#131	1	2	yes	—
249	C₂×C₄	C₁₃×#131	1	2	yes	—
250	C₂×C₄	C₁₃×#131	1	2	yes	—
251	C₈	—	2	4	no	—
252	C₈	—	2	4	no	—
253	C₈	—	4	2	no	—
254	C₈	—	4	2	no	—
255	C₈	—	4	2	no	—
256	C₈	—	4	2	no	—
257	C₂²	C₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
258	C₂²	C₂×C₁₃×#97	1	1	yes	characteristic
259	C₂²	C₄×C₁₃×M₁₆	1	1	yes	characteristic
260	C₂²	C₁₃×#405	1	1	yes	characteristic
261	C₂²	C₁₃×#405	1	1	yes	characteristic
262	C₂²	C₁₃×#405	1	1	yes	characteristic
263	C₂²	C₁₃×#405	1	1	yes	characteristic
264	C₄	—	2	2	no	—
265	C₄	—	2	2	no	—
266	C₄	—	4	1	no	—
267	C₄	—	4	1	no	—
268	C₄	C₁₃×#424	1	2	yes	—
269	C₄	C₁₃×#433	1	2	yes	—
270	C₄	C₁₃×#435	1	2	yes	—
271	C₄	C₁₃×#436	1	2	yes	—
272	C₄	C₁₃×#446	1	2	yes	—
273	C₄	C₁₃×#446	1	2	yes	—
274	C₂	C₁₃×#1451	1	1	yes	characteristic
275	C₂	C₁₃×#1452	1	1	yes	characteristic
276	C₂	C₁₃×#1453	1	1	yes	characteristic
277	C₂	C₁₃×#1454	1	1	yes	characteristic
278	C₂	C₁₃×#1768	1	1	yes	characteristic
279	C₂	C₁₃×#1770	1	1	yes	characteristic
280	C₂	C₁₃×#1771	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²×C₁₃	C₂³
commutator	C₂³	C₂×C₄²×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle, prime radical	C₂³×C₁₃	C₂×C₄²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
50. #8265	C₁₃	direct (N × H)
225. C₁₃	#8265	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₁₃×C₄⋊C₈	2
C₁₃×#1744	2
C₂×C₁₃×#322	2
C₁₃×#1273	2
#8265	13

Subgroups — C13×#8265 #15694604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#8265 #15694604